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Finite Element Analysis of Bi-Metallic Structures with Adhesive Delamination

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Finite Element Analysis of Bi-Metallic Structures with Adhesive Delamination Finite Element Analysis of Bi-Metallic Structures with Adhesive Delamination THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Alisha Ann Cardanini Graduate Program in Welding Engineering The Ohio State University 2017 Master's Examination Committee: Dr. Wei Zhang, Advisor Dr. Avraham Benatar Copyrighted by Alisha Ann Cardanini 2017 Abstract Bi-metal structures made of aluminum and steel are increasingly used for light- weighting applications. Replacing steel parts with aluminum in the body in white can reduce the weight of a vehicle up to 30%. The coefficient of thermal expansion (CTE) of aluminum is almost twice that of steel. Due to such large CTE mismatch, thermal buckling can become a concern when the bi-metal structure is exposed to elevated temperature. When adhesive is added between the aluminum and steel, its curing process can be affected due to buckling of the dissimilar metals. Moreover, stress in the structure developed at high temperature can be permanently locked in when the adhesive fully cures. This can lead to a higher residual gap between the aluminum and the steel than in structures without adhesive. The objective of this research is to quantitatively understand the stress and strain evolution in a bi-metallic Al / adhesive / steel structure exposed to a thermal cycle representative of that used in automotive paint bake process, including delamination of adhesive between the substrates. To achieve this objective, it is essential to first capture the behavior of the bi-metallic structure without adhesive and validating such models. Once validated, addition of cured adhesive and its delamination behavior is then incorporated. Delamination behavior relies on the fracture energy release rate of the ii adhesive material, which is determined through fracture toughness testing. Specially, the research consists of the following two main tasks. First, preliminary finite element models have been developed to capture the behavior of thermal induced buckling, including its deflection profile and stress close to the fasteners. These studies revealed that for a maximum paint bake temperature of 180°C residual stress is only found within the fastening region. This indicates that paint bake process itself does not produce enough heat to exceed elastic strain limits of the bulk structure. Several geometric factors are studied, including plate thickness, fastener pitch, and flange height. These factors reveal the effect of the geometry on the maximum deflection in buckling. Second, adhesive fracture toughness testing is conducted to measure the mode I fracture energy release rate. The fracture toughness is then incorporated in to both lap shear and thermal buckling model. Both use cohesive zone method incorporating linear traction-separation law for modeling the adhesive damage behavior. A hybrid continuum- cohesive element is created to incorporate both delamination effects as well as cured stress locking. The understanding established in this research is essential to optimize the design of bi-metallic structure to control distortion and residual stress in the structure, two important performance properties. Taken as a whole, the research results reported in this thesis represent a first step toward improving the quantitative understanding of adhesive deformation and failure behaviors in Al-steel bi-metallic structure. Future work includes (1) incorporation of non-linear traction-separation behavior in the cohesive elements, and iii (2) testing of adhesive fracture toughness as a function of temperature. Addressing the future work can further improve the accuracy of the computational model. iv Acknowledgments I would like to thank my advisor Wei Zhang for his mentorship and consistent guidance. Thank you for always being available to work with me and holding me to a high standard. You’ve trained me to be an engineer starting from a completely different background and always had faith in my abilities. I would also like to thank Jake Fredrickson for laying down the initial groundwork of my research, and taking the time to introduce me to his work. Thank you to Sean Duan, my undergraduate research assistant, who was always enthusiastic about work and shows promising potential. Thank you to everyone in the welding engineering program who helped teach me testing methods and helped with theoretical discussions. Many thanks to collaborating companies including Honda Research and Development of Americas, Oak Ridge National Lab, Brigham Young University, L&L Products, and DOW Chemical who worked with me closely providing content and ideas for the project. v Vita 2010................................................................California High School 2014................................................................B.S. Applied Mathematics, University of California, Merced 2015 Technical Degree, Hobart School of Welding Technology 2017 ...............................................................M.S. Welding Engineering, The Ohio State University Fields of Study Major Field: Welding Engineering vi Table of Contents Abstract ............................................................................................................................... ii Acknowledgments............................................................................................................... v Vita ..................................................................................................................................... vi Fields of Study ................................................................................................................... vi List of Tables ..................................................................................................................... xi List of Figures ................................................................................................................... xii Chapter 1: Introduction ....................................................................................................... 1 Chapter 2: Literature Review .............................................................................................. 6 2.1 Aluminum to Steel Dissimilar Metal Joining ............................................................ 6 2.1.1 Fusion Welding of Aluminum to Steel ............................................................... 7 2.1.2 Bonded Aluminum/Steel Microstructure............................................................ 8 2.2 Solid State Welding ................................................................................................. 10 2.2.1 Friction Stir Welding ........................................................................................ 11 2.2.2 Friction Bit Joining ........................................................................................... 15 vii 2.3 Epoxy Adhesive ...................................................................................................... 17 2.3.1 Thermosetting Polymers ................................................................................... 21 2.3.2 Fracture Mechanics Theory and Adhesive ....................................................... 23 2.3.3 Epoxy and Adhesion ......................................................................................... 35 2.3.4 Curing of Epoxy Adhesive ............................................................................... 43 2.4 Modeling Adhesives ................................................................................................ 51 2.4.1 Adhesive Curing Modeling .............................................................................. 51 2.4.2 Plasticity of Cured Epoxy ................................................................................. 56 2.4.3 Adhesive Delamination Modeling .................................................................... 58 2.4.4 Traction vs Separation Approach ..................................................................... 61 Chapter 3: Objectives ........................................................................................................ 68 3.1 Model Aluminum/Steel Structures and their Resulting Distortion ......................... 68 3.2 Model Cured Adhesive Delamination ..................................................................... 69 3.3 Fracture Toughness Testing of Adhesive ................................................................ 69 Chapter 4: Modeling of Thermo-Mechanical Buckling .................................................... 71 4.1 Materials .................................................................................................................. 71 4.2 Approach ................................................................................................................. 71 4.2.1 Oven Experiment .............................................................................................. 72 viii 4.2.2 FEM Model....................................................................................................... 73 4.2.2.1 Model Assumptions .................................................................................. 74 4.2.2.2 Model Approach ....................................................................................... 74 4.3 Results and Discussion ............................................................................................ 79 4.3.1 Plate Thickness Analysis .................................................................................
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